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Abstract
The aim of this work is to study the problem of detection of sources in discrete distributed systems. We characterize discrete detectable sources and spy sensors and we give the relationship between these sensors and strategic sensors. Then we show how to reconstruct a detectable source from the corresponding output, in the cases where the observation is exact or affected by an observation error. In the case of sources located in a subregion of the geometrical support of the considered system, we study the problem of regional detection and reconstruction of discrete sources. Examples and numerical results are also given.
Acknowledgments
A. El Jai is Professor at the University of Perpignan in France. He was Professor at the Faculty of Sciences of Rabat in Morocco (1979–1985) and Assistant Professor at the University Paul Sabatier in Toulouse, France (1971–1979). He obtained his doctorat d’Etat in Automatic Control (1978) at LAAS, Toulouse. His research work on linear DPS has brought hundred of papers, 5 books and more than fourty PhD students.
L. Afifi is a Professor at the Faculty of Sciences, Department of Mathematics and Computer Science (Head of Department), University Hassan II Ain Chock, Casablanca, Morocco. He obtained his doctorat d’Etat in Analysis and Control Theory (1994) at the University Ibn Tofail, Kenitra. His research work interests are essentially in Distributed Parameter Systems (DPS). Currently, he is the director of the laboratory: Analysis and Control of Systems in the same institution.
M. Merry obtained his doctorat in the Faculty of Sciences (2000), Department of Mathematics and Computer Science, University Hassan II Ain Chock, Casablanca, Morocco. Here research interests are in the areas of Distributed Parameter Systems and control theory, particularly in detection and inverse problems. Currently, she is in the Moroccan ministry of planning, section of Casablanca.